Comparison of the Glover Solution with the Simultaneous-Equations Approach for Measuring Hydraulic Conductivity
The Glover solution and the simultaneous-equations approach have been suggested for determining the saturated hydraulic conductivity (Ks) of the vadose zone by the constant-head well permeameter technique. The objective of this paper is to examine the two procedures and discuss the uncertainty associated with calculating Ks by the simultaneous-equations approach (referred to as Kfs) as compared with using the Glover solution. Two flow regions are identified with the constant heights of water, H1 and H2 (H2 > H1), at the bottom of an auger hole of radius r during measurements of steady state flow rates, Q1 and Q2. The Ks's over the distances H1 (lower region), H2 – H1 (upper region), and H2 (entire wetted zone) at the bottom of the hole are designated as Ksl, Ksu, and Ksc, respectively. Using the Glover solution for calculating Ksl and Ksc for a homogeneous and isotropic medium, an equation is developed for calculating Ksu based on Q1, H1, Q2, H2, and r. This equation is found to be very similar to the equation for calculating Kfs by simultaneous-equations approach. It is shown that Ksl > Ksc whenever the Kfs value is negative. Conversely, the matric flux potential calculated by the simultaneous-equations approach (φm) is negative only when Ksc > Ksl. This is significant because, in the simultaneous-equations approach, the Kfs value will not be acceptable when φm is negative. The Glover solution (i.e., equation to calculate Ksc or Ksl) is applicable to both homogeneous and heterogeneous soils and does not yield a negative value, whereas the simultaneous-equations approach can only yield reliable results for homogeneous and isotropic media.
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